Dynamics And Synchronization Analysis Of Fractional Order Delayed Coupled Memristive Chaotic System

Since HP Labs successfully developed a nanometer memristor device entity with two layers of titanium dioxide thin film materials,new types of nonlinear memristors have gradually emerged in different fields such as chaos.Through in-depth research on memristors,it is found that when multiple memristors are connected in different topologies,it is inferred that there is coupling behavior between memristors based on electromagnetic characteristics.And the coupling is the third connection relationship between the two state variables(magnetic flux and charge)in addition to the series and parallel connections between the memristors.Due to the nonlinear time-varying characteristics of the memristor,the complex memristor chaotic circuit composed of multiple memristors exhibits more complicated chaotic characteristics.Fractional calculus as an effective and powerful mathematical modeling tool can accurately describe and reveal the essential characteristics of things.Therefore,this paper uses fractional order theory to model the memristive chaotic circuit,and considers the existence of time delay in the actual circuit and the coupling behavior between multiple memristors to construct two types of fractional order delay coupled memristive chaotic systems.It is of great theoretical significance to study the dynamics and synchronization of fractional-order time-delay coupled memristive chaotic system,and it also shows extremely high application value in secure communication.The main contents of this paper are summarized as follows:(1)Study the influence of the coupling behavior between memristors on the dynamics of the coupled memristor system.Based on the detailed introduction of the coupling characteristics of the flux-controlled memristor in parallel configuration,combined with the Chua's chaotic circuit,the coupled memristor chaotic system is derived,and then the dynamic analysis results relying on the coupling strength of the memristor indicate that proper adjustment of the coupling strength can be effective control the chaotic behavior of the system.(2)Take the coupled memristive chaotic system as the research object,introduce the time-delay factor,then apply the fractional order theory to generalize it to the fractional-order model,and then use the coupling strength,fractional order and delay as controllable parameters studying the dynamic behavior of the system,it is found that the dynamic characteristics of the fractional order system are more abundant and complex,and the coupling strength can change the chaotic behavior of the system,but the time delay introduced will not affect the system state.(3)Analyze the attractor and synchronization problems of a fractional-order coupled memristive chaotic system without equilibrium points.By changing the system parameters and choosing different initial values to study the dynamics of the system,it is found that the system produces hiddenattractors and coexisting attractors.At the same time,according to the stability theorem of the fractional nonlinear system,a simple and effective active control method is proposed,which solves the synchronization problem based on the system,and the synchronization rate of the error system is discussed by changing the size of the system parameters,fractional order and time-delay values.Finally,the experimental simulation results verify the correctness of the theoretical analysis.